The corona G◦H of two graphs G and H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining each i-th vertex of G to every vertex in the i-th copy of H. The neighborhood coronaG⋆H of two graphs G and H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining the neighbors of the i-th vertex of G to every vertex in the i-th copy of H. In this p...

Let G be a k-degenerate graph of order n. It is well-known that G has no more edges than Sn,k, the join of a complete graph of order k and an independent set of order n−k. In this note, it is shown that Sn,k is extremal for some spectral parameters of G as well. More precisely, letting μ (H) and q (H) denote the largest eigenvalues of the adjacency matrix and the signless Laplacian of a graph H...

This paper gives tight upper bound on the largest eigenvalue q (G) of the signless Laplacian of graphs with no paths of given order. Thus, let Sn,k be the join of a complete graph of order k and an independent set of order n− k, and let S n,k be the graph obtained by adding an edge to Sn,k. The main result of the paper is the following theorem: Let k ≥ 1, n ≥ 7k, and let G be a graph of order n...